Transcription of Quantum Mechanics
1 Quantum MechanicsSecond EditionQuantum MechanicsConcepts and ApplicationsSecond EditionNouredine ZettiliJacksonville State University, Jacksonville, USAA John Wiley and Sons, Ltd., PublicationCopyright 2009 John Wiley & Sons, LtdRegistered officeJohn Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United KingdomFor details of our global editorial offices, for customer services and for information about how to apply forpermission to reuse the copyright material in this book please see our website at right of the author to be identified as the author of this work has been asserted in accordance with theCopyright, Designs and Patents Act rights reserved.
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3 The publisher is not associated with any product or vendor mentionedin this book. This publication is designed to provide accurate and authoritative information in regard to thesubject matter covered. It is sold on the understanding that the publisher is not engaged in renderingprofessional services. If professional advice or other expert assistance is required, the services of a competentprofessional should be of Congress Cataloging-in-Publication DataZettili, Mechanics : concepts and applications / Nouredine Zettili. 2nd bibliographical references and 978-0-470-02678-6 (cloth: alk. paper) ISBN 978-0-470-02679-3 (pbk.)
4 : alk. paper)1. Quantum theory. I. dc222008045022A catalogue record for this book is available from the British LibraryProduced from LaTeX files supplied by the authorPrinted and bound in Great Britain by CPI Antony Rowe Ltd, Chippenham, WiltshireISBN: 978-0-470-02678-6 (H/B)978-0-470-02679-3 (P/B)ContentsPreface to the Second EditionxiiiPreface to the First EditionxvNote to the Studentxvi1 Origins of Quantum HistoricalNote .. ParticleAspectofRadiation .. Blackbody Radiation .. Pair Production .. WaveAspectofParticles .. de Broglie s Hypothesis: Matter Waves .. Experimental Confirmation of de Broglie s Hypothesis.
5 MatterWavesforMacroscopicObjects .. ParticlesversusWaves .. Wave Particle Duality: Complementarity .. Principle of Linear Superposition .. IndeterministicNatureoftheMicrophysicalW orld .. Heisenberg sUncertaintyPrinciple .. AtomicTransitionsandSpectroscopy .. Rutherford Planetary Model of the Atom .. Bohr Model of the Hydrogen Atom .. QuantizationRules .. WavePackets .. LocalizedWavePackets .. MotionofWavePackets .. ConcludingRemarks .. 71vviCONTENTS2 Mathematical Tools of Quantum Introduction .. TheHilbertSpace .. DimensionandBasisofaVectorSpace .. Square-Integrable Functions: Wave Functions.
6 DiracNotation .. Operators .. General HermitianAdjoint .. ProjectionOperators .. Uncertainty Relation between Two Operators .. Functions of Operators .. InverseandUnitaryOperators .. EigenvaluesandEigenvectorsofanOperator .. InfinitesimalandFiniteUnitaryTransformat ions .. Matrix Representation of Kets, Bras, and Operators .. Change of Bases and Unitary Transformations .. Matrix Representation of the Eigenvalue Problem .. Representation in Continuous Bases .. GeneralTreatment .. PositionRepresentation .. Connecting the Position and Momentum Representations .. MatrixandWaveMechanics.
7 MatrixMechanics .. WaveMechanics .. ConcludingRemarks .. SolvedProblems ..1553 Postulates of Quantum Introduction .. TheBasicPostulatesofQuantumMechanics .. Probability Density .. The Superposition Principle .. MeasurementinQuantumMechanics .. HowMeasurementsDisturbSystems .. Complete Sets of Commuting Operators (CSCO) .. Measurement and the Uncertainty Relations .. TimeEvolutionoftheSystem Stationary States: Time-Independent Potentials .. Schr dinger Equation and Wave Packets .. The Conservation of Probability .. SymmetriesandConservationLaws .. ConnectingQuantumtoClassicalMechanics.
8 PoissonBracketsandCommutators .. Quantum Mechanics and Classical Mechanics .. SolvedProblems ..2094 One-Dimensional Introduction .. Discrete Spectrum (Bound States) .. Continuous Spectrum (Unbound States) .. MixedSpectrum .. The Free Particle: Continuous States .. ThePotentialBarrierandWell .. The CaseE The CaseE V0: Tunneling .. The InfiniteSquareWellPotential .. TheAsymmetricSquareWell .. The Scattering Solutions (E V0).. The Bound State Solutions (0 E V0).. The Harmonic Oscillator .. EnergyEigenstatesinPositionSpace .. The Matrix Representation of Various Operators .. Expectation Values of Various Operators.
9 Numerical Solution of the Schr dinger Equation ..276viiiCONTENTS5 Angular Introduction .. Orbital Angular Momentum .. General Formalism of Angular Momentum .. Matrix Representation of Angular Momentum .. Geometrical Representation of Angular Momentum .. Spin Angular Momentum .. Experimental Evidence of the Spin .. Spin 1 2andthePauliMatrices .. Eigenfunctions of Orbital Angular Momentum .. Eigenfunctions and Eigenvalues of Eigenfunctions of ; Properties of the Spherical Harmonics .. SolvedProblems .. Exercises ..3256 Three-Dimensional Introduction .. 3D Problems in Cartesian Coordinates.
10 General Treatment: Separation of Variables .. TheBoxPotential .. The Harmonic Oscillator .. 3D Problems in Spherical Coordinates .. CentralPotential:GeneralTreatment .. The Free Particle in Spherical Coordinates .. The Isotropic Harmonic Oscillator .. TheHydrogenAtom .. Effect of Magnetic Fields on Central Potentials .. ConcludingRemarks .. SolvedProblems .. Exercises ..3857 Rotations and Addition of Angular RotationsinClassicalPhysics .. PropertiesoftheRotationOperator .. Rotation Matrices and the Spherical Harmonics .. Addition of Angular Momenta .. Addition of Two Angular Momenta: General Formalism.
